Question

Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed along parallel lines. At a particular instant, and are thir respective position vectors drawn from point A which is in the plane of the parallel lines. Which of the following is the correct statement?

• A. Angular momentum of particle 1 about A is
• B. Angular momentum L2 of particle 2 about A is
• C. Total angular momentum of the system about A is
• D. Total angular momentum of the system about A is $\overrightarrow { \mathrm { L } } = \operatorname { mv } \left( \mathrm { d } _ { 2 } - \mathrm { d } _ { 1 } \right) \otimes$ $\otimes$represents a unit vector going into the page. $\Theta$represents a unit vector coming out of the page?

Answer 1

Answer: (D)

Total angular momentum of the system about A is

$\overrightarrow { \mathrm { L } } = \operatorname { mv } \left( \mathrm { d } _ { 2 } - \mathrm { d } _ { 1 } \right) \otimes$

$\otimes$represents a unit vector going into the page.

$\Theta$represents a unit vector coming out of the page?

Answer 2

Angular momentum of particle 1 about A is,

$\overrightarrow { \mathrm { L } } _ { 1 } = \operatorname { mvd } _ { 1 } \Theta$

Angular momentum of particle 2 about A is,

$\overrightarrow { \mathrm { L } } _ { 2 } = \operatorname { mvd } _ { 2 } \otimes$

$\therefore$ total angular momentum of the system about A is , $\overrightarrow { \mathrm { L } } = \overrightarrow { \mathrm { L } } _ { 2 } - \overrightarrow { \mathrm { L } } _ { 1 }$ ( $\mathrm { L } _ { 1 }$ and $\mathrm { L } _ { 2 }$ are in opposite directions

$\overrightarrow { \mathrm { L } } = \operatorname { mv } \left( \mathrm { d } _ { 2 } - \mathrm { d } _ { 1 } \right) \otimes$